Maths-

General

Easy

Question

# Write the solutions to the given equation.

Rewrite them as the linear-quadratic system of equations and graph them to solve.

Hint:

### A quadratic equation is when the polynomial has a degree two. A graph is a geometrical representation of an equation.

We are asked to solve the equation graphically by arranging them in a linear-quadratic equation.

## The correct answer is: We are asked to solve the equation graphically by arranging them in a linear-quadratic equation.

### Step 1 of 2:

The given equation is .

Re arranging them, we get:

Here, once we rearrange it, we multiply the equation with ten to remove the decimal. Then, take out five to factorize into the simplest form.

Step 2 of 2:

Graph the equation to get the solution:

.

Thus, the solution of the equation is:

.

A lot of the quadratic equations can be solved using identities and factorization. You would get a maximum of two solutions for each quadratic equation.

### Related Questions to study

Maths-

### Prove the following statement.

The length of any one median of a triangle is less than half the perimeter of the triangle.

Answer:

c < a + b

solution:

Side AB = a

Side BC = b

Side AC = c

And median AM be M

AM is median so M is midpoint of BC

BM =

So, according to triangle inequality theorem,

M

In △ACM,

AM is median so M is midpoint of BC

MC =

So, according to triangle inequality theorem,

M

Add eq. 1 and eq. 2.

M

2M

M

- Hints:
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c

c < a + b

- The line segment which joins the vertex of triangle to midpoint of opposite side is called the ‘median’.
- Perimeter of triangle is sum of sides.
- Perimeter = a + b + c
- To prove:
- The length of any one median of a triangle is less than half the perimeter of the triangle.

solution:

- Step 1:

Side AB = a

Side BC = b

Side AC = c

And median AM be M

_{a}- Step 2:

AM is median so M is midpoint of BC

BM =

So, according to triangle inequality theorem,

M

_{a}< a + ---- eq. 1In △ACM,

AM is median so M is midpoint of BC

MC =

So, according to triangle inequality theorem,

M

_{a}< c + ---- eq. 2Add eq. 1 and eq. 2.

M

_{a}+ M_{a}< a + + c +2M

_{a}< a + b + cM

_{a}<- Final Answer:

### Prove the following statement.

The length of any one median of a triangle is less than half the perimeter of the triangle.

Maths-General

Answer:

c < a + b

solution:

Side AB = a

Side BC = b

Side AC = c

And median AM be M

AM is median so M is midpoint of BC

BM =

So, according to triangle inequality theorem,

M

In △ACM,

AM is median so M is midpoint of BC

MC =

So, according to triangle inequality theorem,

M

Add eq. 1 and eq. 2.

M

2M

M

- Hints:
- Triangle inequality theorem
- According to this theorem, in any triangle, sum of two sides is greater than third side,
- a < b + c

c < a + b

- The line segment which joins the vertex of triangle to midpoint of opposite side is called the ‘median’.
- Perimeter of triangle is sum of sides.
- Perimeter = a + b + c
- To prove:
- The length of any one median of a triangle is less than half the perimeter of the triangle.

solution:

- Step 1:

Side AB = a

Side BC = b

Side AC = c

And median AM be M

_{a}- Step 2:

AM is median so M is midpoint of BC

BM =

So, according to triangle inequality theorem,

M

_{a}< a + ---- eq. 1In △ACM,

AM is median so M is midpoint of BC

MC =

So, according to triangle inequality theorem,

M

_{a}< c + ---- eq. 2Add eq. 1 and eq. 2.

M

_{a}+ M_{a}< a + + c +2M

_{a}< a + b + cM

_{a}<- Final Answer:

General

### Select the three most common text features

Correct answer a) Title, 6) Table of Content d) Picture of and Captions

Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body

Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body

### Select the three most common text features

GeneralGeneral

Correct answer a) Title, 6) Table of Content d) Picture of and Captions

Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body

Explanations - Text features refer to parts of a text but don't necessarily appear directly within the main body

Maths-

### Solve 3.5x+19≥1.5x-7

Hint:

Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .

We are asked to solve the inequality.

Step 1 of 1:

Rearrange and solve the inequality,

Note:

Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.

Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .

We are asked to solve the inequality.

Step 1 of 1:

Rearrange and solve the inequality,

Note:

Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.

### Solve 3.5x+19≥1.5x-7

Maths-General

Hint:

Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .

We are asked to solve the inequality.

Step 1 of 1:

Rearrange and solve the inequality,

Note:

Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.

Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .

We are asked to solve the inequality.

Step 1 of 1:

Rearrange and solve the inequality,

Note:

Whenever we use the symbol ≤ or ≥ , we use the endpoint as well. We could also solve the inequality by graphing it.

Maths-

### Determine whether each graph represents a function ?

*Step by step solution:*

We consider the first graph.

We can observe that any vertical line drawn on the graph cuts the line at exactly one point

Hence, this graph represents a function.

The second graph is

Again, we can observe that any vertical line drawn cuts the graph at exactly one point.

Hence, this graph is also a function.

Finally, consider the third graph.

If we draw a vertical line at the origin, that is, the y-axis, we can see that it cuts the graph at two points.

Thus, this graph is not a function.

### Determine whether each graph represents a function ?

Maths-General

*Step by step solution:*

We consider the first graph.

We can observe that any vertical line drawn on the graph cuts the line at exactly one point

Hence, this graph represents a function.

The second graph is

Again, we can observe that any vertical line drawn cuts the graph at exactly one point.

Hence, this graph is also a function.

Finally, consider the third graph.

If we draw a vertical line at the origin, that is, the y-axis, we can see that it cuts the graph at two points.

Thus, this graph is not a function.

General

### Choose the negative adjectives starting with ' u '

Correct answer a) unattractive.

Explanation-Negative adjectives are the word that explains / pronounce negatively.

Explanation-Negative adjectives are the word that explains / pronounce negatively.

### Choose the negative adjectives starting with ' u '

GeneralGeneral

Correct answer a) unattractive.

Explanation-Negative adjectives are the word that explains / pronounce negatively.

Explanation-Negative adjectives are the word that explains / pronounce negatively.

Maths-

### Describe the possible values of x.

- Step-by-step explanation:

- Given:

a = x + 11, b = 2x + 10, and c = 5x - 9.

- Step 1:
- First check validity.

According to triangle inequality theorem,

c - b < a < b + c,

(5x – 9) – (2x + 10) < x + 11 < (2x + 10) + (5x – 9)

3x - 19 < x + 11 < 7x + 1

First consider,

x + 11 < 7x + 1,

11 – 1 < 7x - x

10 < 6x

< x,

1.6 < x

Now, consider,

3x - 19 < x + 11

3x - x < 11 + 19

2x < 30

x < ,

x < 15

therefore,

1.6 < x < 15

- Final Answer: